Details

Time bar (total: 1.2m)

sample86.0ms

Algorithm
intervals
Results
46.0ms298×body80valid
14.0ms104×body80nan

simplify178.0ms

Calls
1 calls:
Slowest
178.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize37.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
4.2b
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
3.5b
(/ (* M D) (* 2 d))
3.5b
(/ (* M D) (* 2 d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
26×add-cbrt-cube add-exp-log
11×cbrt-undiv div-exp
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×div-inv
4×pow1 prod-exp cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod associate-/l* associate-/l/
2×sqrt-div
1×frac-times rem-sqrt-square flip3-- pow1/2 associate-*l/ associate-*r/ associate-/r/ flip--
Calls
4 calls:
Slowest
12.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
3.0ms
(/ (* M D) (* 2 d))
3.0ms
(/ (* M D) (* 2 d))
2.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

series241.0ms

Calls
4 calls:
Slowest
123.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
82.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
18.0ms
(/ (* M D) (* 2 d))
18.0ms
(/ (* M D) (* 2 d))

simplify12.7s

Calls
52 calls:
Slowest
2.1s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
1.4s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
1.0s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
615.0ms
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))
514.0ms
(sqrt (- (pow 1 3) (pow (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h)) 3)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize20.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (/ (* M D) (* 2 d)) (/ 1 h))
4.2b
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
4.2b
(/ (/ (* M D) (* 2 d)) l)
3.5b
(/ (* M D) (* 2 d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
27×times-frac
18×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
15×div-inv
11×add-cbrt-cube add-exp-log associate-/l*
5×associate-/r*
4×pow1 cbrt-undiv div-exp insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod
2×sqrt-div associate-/l/
1×rem-sqrt-square flip3-- pow1/2 associate-/r/ flip--
Calls
4 calls:
Slowest
10.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
6.0ms
(/ (/ (* M D) (* 2 d)) l)
3.0ms
(/ (* M D) (* 2 d))
1.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

series200.0ms

Calls
4 calls:
Slowest
116.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
36.0ms
(/ (/ (* M D) (* 2 d)) l)
32.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
16.0ms
(/ (* M D) (* 2 d))

simplify11.1s

Calls
80 calls:
Slowest
769.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
679.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
617.0ms
(sqrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) 3)))
589.0ms
(sqrt (- (* 1 1) (* (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))))))
485.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
4.2b
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
4.2b
(/ (/ (* M D) (* 2 d)) l)
3.5b
(/ (* M D) (* 2 d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
22×times-frac
18×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
15×div-inv
13×add-exp-log
11×associate-/l*
8×add-cbrt-cube
6×associate-/r/
5×associate-/r* div-exp
4×pow1 insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod
2×cbrt-undiv rec-exp sqrt-div associate-/l/
1×rem-sqrt-square flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
10.0ms
(/ (/ (* M D) (* 2 d)) l)
5.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
3.0ms
(/ (* M D) (* 2 d))
1.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))

series246.0ms

Calls
4 calls:
Slowest
137.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
47.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
43.0ms
(/ (/ (* M D) (* 2 d)) l)
19.0ms
(/ (* M D) (* 2 d))

simplify16.3s

Calls
78 calls:
Slowest
705.0ms
(sqrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))
611.0ms
(/ (sqrt (/ 1 (/ (* 2 d) (* M D)))) (/ 1 h))
538.0ms
(/ (sqrt (/ 1 (/ (* 2 d) (* M D)))) (sqrt (/ 1 h)))
514.0ms
(sqrt (- (* 1 1) (* (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))))))
514.0ms
(/ (* (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 (/ (* 2 d) (* M D))))) 1)

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize21.0ms

Local error

Found 4 expressions with local error:

5.8b
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
5.8b
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
5.8b
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
4.5b
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
20×times-frac
18×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×div-inv
11×add-exp-log
9×cbrt-prod
6×cbrt-div add-cbrt-cube associate-/r/
5×associate-/l*
4×pow1 associate-/r* div-exp insert-posit16 add-log-exp
3×flip3-- pow1/3 flip--
2×rec-exp
1×cbrt-undiv clear-num frac-2neg associate-/l/
Calls
4 calls:
Slowest
5.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
1.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
1.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
1.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))

series707.0ms

Calls
4 calls:
Slowest
240.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
218.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
203.0ms
(cbrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h)))))
46.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))

simplify18.9s

Calls
78 calls:
Slowest
726.0ms
(exp (* 1/3 (- (+ (log (/ -1 l)) (+ (* 2 (log (/ -1 d))) (log -1/4))) (+ (* 2 (log (/ -1 M))) (+ (* 2 (log (/ -1 D))) (log (/ -1 h)))))))
644.0ms
(cbrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))
596.0ms
(cbrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))
558.0ms
(cbrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))) 3)))
552.0ms
(/ (cbrt (/ 1 (/ (* 2 d) (* M D)))) (sqrt (/ 1 h)))

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

regimes1.5s

Accuracy

0% (1.4b remaining)

Error of 8.7b against oracle of 7.3b and baseline of 8.7b

bsearch21.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.8s9310×body80valid
653.0ms3150×body80nan